For the graph shown, select the statement that best represents the given system of equations.
Number graph ranging from negative five to five on the x axis and negative six to four on the y axis. A line with a negative slope is drawn on the graph.
6x + 4y = 2
3x + 2y = 1

A.
not enough information

B.
coincident

C.
consistent and independent

D.
inconsistent

After analyzing the data provided in this question one can conclude that they are coincident. For the first system equation we have: 6x + 4y = 2. If we divide everything by 2 we will get: 3x + 2y = 1. Coincident means the same line.

The answer is choice B). Coincident.

I hope it helps, Regards.

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jajumonac jajumonac · Answer 2 · 2020-01-08T03:54:49+01:00

Answer:

B. coincident

Step-by-step explanation:

An coincident system of equations means that it has infinite solutions, because one line is on the other one. This happens when their equation are the same, or their "parent" line is the same.

So, given equations are:

6x + 4y = 2 and 3x + 2y = 1

Observe that if we divide the first by 2, we have

[tex]\frac{6x + 4y}{2}=\frac{2}{2}\\\frac{6x}{2}+\frac{4y}{2}=1\\ 3x+2y=1[/tex]

As you can see, using the first equation, we found that it has the same "parent" equation than the second equation. In other words, they are basically the same. This means that they represent the same line, so, the system is coincident and they have infinite solutions.